@RFD Are you using our Next Gen UI for Expense Reports or are you using our legacy UI?
If you are using our legacy UI, then with your expense report open, click on each mileage line item (click the little checkbox to the left). You should see some options appear on the right (where your list of expense types would be). One of the options says Edit. Click this link. It will bring up a window with fields that can be edited. Enter your business purpose here. This will update all selected entries.
If you are using our Next Gen UI, the ability to edit multiple entries is not availble.
@RFD if when you create a new expense report, if it looks like my screenshot below, then you are on the next generation or the new UI.